The generator matrix

1 0 0 0 0 1 1 1 2 0 1 1 0 1 2 1 2 1 0 1 1 1 0 1 2 0 2 0 1 1 2 1 1 2 0 1 2 1
0 1 0 0 0 0 0 0 0 0 0 2 1 1 1 3 2 3 1 3 3 1 1 2 0 1 1 0 1 2 2 3 1 1 1 1 2 3
0 0 1 0 0 0 1 1 1 2 0 0 0 0 0 2 2 2 3 3 1 1 1 1 1 2 0 1 3 3 2 0 2 3 1 0 1 2
0 0 0 1 0 1 0 1 3 2 2 1 1 3 1 2 1 2 1 1 2 1 1 0 2 3 2 1 3 0 1 3 3 0 0 3 1 0
0 0 0 0 1 1 3 2 1 1 1 0 2 1 1 0 1 1 2 0 2 1 3 0 1 1 3 0 2 1 1 3 3 2 2 3 2 1
0 0 0 0 0 2 2 0 2 2 0 2 2 2 0 2 2 0 0 0 2 2 2 2 0 2 2 2 2 2 0 2 0 2 0 0 0 2

generates a code of length 38 over Z4 who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+80x^31+128x^32+136x^33+165x^34+150x^35+161x^36+182x^37+163x^38+138x^39+133x^40+126x^41+141x^42+110x^43+73x^44+66x^45+41x^46+30x^47+14x^48+2x^49+2x^50+4x^51+2x^52

The gray image is a code over GF(2) with n=76, k=11 and d=31.
This code was found by Heurico 1.10 in 201 seconds.